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Thread: Vector equations in R^3

  1. #1
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    Question Vector equations in R^3

    Hi,

    I'm trying to understand the question below:

    Vector equations in R^3-screen-shot-2018-01-27-10.23.47-pm.png

    The solution is:
    Vector equations in R^3-screen-shot-2018-01-27-10.26.08-pm.png

    Can someone explain how the parametric vector equation for 'z' was created? Also, how do you know what a "suitable restriction" is ?

    - otownsend
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  2. #2
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    Re: Vector equations in R^3

    Quote Originally Posted by otownsend View Post
    Click image for larger version. 

Name:	Screen Shot 2018-01-27 at 10.23.47 PM.png 
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    The solution is: Click image for larger version. 

Name:	Screen Shot 2018-01-27 at 10.26.08 PM.png 
Views:	2 
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ID:	38493
    Here is such a line: $\ell(t)-\left\{ \begin{array}{l}-3t\\t\\3-6t\end{array} \right.$

    Is it true that $A=\ell(-2)~\&~B=\ell(5)~?$
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  3. #3
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    Re: Vector equations in R^3

    The line must pass through the point (0, 0, 3) and have direction vector (-1, 3, -6). Then x= 0+ (-1)t= -t, y= 0+ 3t= 3t, and z= 3+ (-6)t= 3- 6t work.

    In general, the line passing through $(x_0, y_0, z_0)$ with direction vector (A, B, C) has parametric equations $x= x_0+ At$, $y= y_0+ Bt$, and $z= z_0+ Ct.
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